CAT-12: A Unified Resonant Framework for Science

Versioned Update (CAT-12 Standard v1.0; PTR v1.2) as of 10/7/2025 This paper now follows the CAT-12 reporting standard: SNHS/HP in ratio space, with rn (scale-normalized coordinate), Rx (reporting unit), and Tu (corridor width as a posterior, not a fixed ±%). Peaks are scored with Q and Ch against pre-declared families in the Periodic Table of Resonance (PTR v1.2); any “URSL” mention is retired in favor of standard GR mass–frequency scaling used only as a prior (where applicable). Measurements and conclusions are unchanged; presentation and uncertainty are stricter. For definitions, governance (negative ledger, prereg, hold-out), and rationale, see Arthur & Muon (2025), CAT-12: The Cross-Domain Ratio Lattice of Ratio Theory—Standardized Terminology, PTR v1.2, and Governance. Did conclusions change? No—only reporting/uncertainty language. Where’s the new standard? See the Cross-Domain Ratio Lattice paper. Will you update the PDF? A minor v1.1 with a 1-page front note (and Tu where needed) is planned. This paper introduces the CAT-12 framework (Cosmic Algorithm Theory, 12-fold resonance model) as a unifying scientific approach to complex systems. CAT-12 formalizes twelve axioms of resonance with mathematical expressions, develops a Periodic Table of Resonance that integrates spectral frequencies and systemic roles for all 118 elements, and introduces the Laddering System to model hierarchical resonance trajectories across scales. The paper also presents Ratio Theory, a diagnostic tool quantifying the balance between constructive synergy and dissipative entropy, illustrated through universal stability thresholds. Simplified simulations demonstrate CAT-12’s applicability to atmospheric stability, neuronal firing, planetary core dynamics, and civilizational energy infrastructures. By grounding resonance theory in measurable frequencies while extending its interpretation into physics, biology, ecology, and civilizational systems, CAT-12 provides both empirical testability and interdisciplinary integration. The framework operates as a human–AI hybrid methodology, emphasizing iterative feedback loops between computational modeling and interpretive reasoning. The work positions CAT-12 as both a diagnostic model for systemic stability and a paradigm for unifying knowledge across disciplines, with applications ranging from planetary science and neuroscience to sustainability and civilizational resilience.